Konstantin Zarembo

The Bethe-ansatz for Script N = 4 super Yang-Mills

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhins to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.

Stringing Spins and Spinning Strings

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N = 4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L 2J,J], interpolate smoothly between the BMN case of two impurities (J = 2) and the extreme case where the number of impurities equals half the total number of fields (J = L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L 2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.

The Algebraic Curve of Classical Superstrings on AdS5×S5

We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS5×S5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop supersymmetric gauge theory proving the complete agreement of spectra in this approximation.

Yang-Mills duals for semiclassical strings on AdS5 × S5

We consider a semiclassical multiwrapped circular string pulsating on S5, whose center of mass has angular momentum J on an S3 subspace. Using the AdS/CFT correspondence we argue that the one-loop ...

Exact solution of quantum field theory on noncommutative phase spaces

We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an inter ...

Matching quantum strings to quantum spins: One-loop vs. finite-size corrections

Abstract We compare quantum corrections to semiclassical spinning strings in AdS 5 × S 5 to one-loop anomalous dimensions in N = 4 supersymmetric gauge theory. The latter are computed using the reduced (Landau–Lifshitz) sigma model and with the help of the Bethe ansatz. The results of all three approaches are in remarkable agreement with each other. As a byproduct we establish the relationship between linear instabilities in the Landau–Lifshitz model and analyticity properties of the Bethe ansatz.

Quantum corrections to spinning strings in AdS5xS5 versus Bethe ansatz: a comparative study

We analyze quantum corrections to rigid spinning strings in AdS5 × S5. The one-loop worldsheet quantum correction to the string energy is compared to the finite-size correction from the quantum string Bethe ansatz. Expanding the summands of the string theory energy shift in the parameter 1/2 and subsequently resumming them yields a divergent result. However, upon zeta-function regularisation these results agree with the Bethe ansatz in the first three orders. We also perform an analogous computation in the limit of large winding number, which results in a disagreement with the string Bethe ansatz prediction. A similar mismatch is observed numerically. We comment on the possible origin of this discrepancy.

B-field in AdS 3 / CF T 2 correspondence and integrability

A bstractWe construct topological Wess-Zumino term for supercoset sigma-models on various AdS3 backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappa-symmetry and conformal invariance are equivalent to each other.

Localization techniques in quantum field theories

This is the foreword to the special volume on localization techniques in quantum field theory. We summarize the individual chapters and their relation.

Bethe ansatz in stringy sigma models

We compute the exact S-matrix and give the Bethe ansatz solution for three sigma-models which arise as subsectors of string theory in AdS(5)xS(5): Landau-Lifshitz model (non-relativistic sigma-model on S(2)), Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and Faddeev-Reshetikhin model (string sigma-model on S(3)xR).